Subject: UHF-CISD

From: [email-masked] (Mike Frisch)
Date: Wed, 17 May 1995 09:34:03 -0400 (EDT)

Ayaz Bakasov, Phys. Chem., ETH Zurich writes:

      I have to calculate expectation values of an operator
      which is nonzero if:

      1) Neither alpha- nor beta- spin component of the wave
         function is CONSTANT (including zero), i.e. both spin
         components are non-trivial functions of coordinates;

      2) The alpha- and beta- spin components of the wave
         function are not equal to each other (i.e. are
         different functions of coordinates).

      It is highly desirable to have better wave function, such
      as CI. However, the CI available, for instance, from
      G92/94, is based on the RHF reference determinant.  It
      means that whatever CI I will produce, this will be a
      combination of determinants with zero (or equal) alpha or
      beta spin component for a given spatial molecular orbital.

      If UHF gives already non-zero, are there CI (or analogous
      methods) available which are based on the UHF reference
      determinant ???

Actually, the open-shell CISD code is Gaussian IS based on a UHF
rather than an RHF reference determinant, and you can get the
appropriate alpha and beta generalized density matrices if you wish to
computer properties.  So, I think this is just what you want.

While we're on the subject, I'd like to clear up a related
misconception which I've seen in the literature.  The UCISD
wavefunction in Gaussian is NOT an exact spin eigenfunction.  It
consists of all determinants produced by replacing one or two
spin-orbitals which are occupied in the reference determinant with
virtuals.  For an open-shell system, this would not lead to a
spin-eigenfunction even if the reference determinant had the same
alpha and beta orbitals, because some determinants which are a double
excitation over spacial orbitals but a triple excitation over
spin-orbitals (because the spins are flipped) are needed to form
proper spin-eigenfunctions.

To show a simpler example with singles vs. doubles, if the reference
determinant is 1a 1b 2a, then the determinant 1a 2a 3b is considered a
single excitation over spin-orbitals but 1a 2b 3a, which should be
mixed with 1a 2a 3b to form a spin-eigenfunction, is a double
excitation of spin-orbitals from the reference.  Of course, both of
these would be included in a CISD wavefunction, but the same issue
occurs with double and triple excitations.

All of these problems are specific to the open-shell case and the
closed-shell CISD wavefunction in Gaussian is a proper
spin-eigenfunction.  Also, note that for most properties of either
closed or open-shell systems, QCISD is considerably more accurate than
CISD with a modest difference in cost and is to be preferred.

Mike Frisch
Lorentzian, Inc.
[email-masked]